Anonymous user
Cramer's rule: Difference between revisions
→{{header|Maxima}}
Line 1,693:
(%o6) [w = 2, x = - 12, y = - 4, z = 1]
</lang>
=={{header|Nim}}==
{{trans|Phix}}
<lang Nim>type
SquareMatrix[N: static Positive] = array[N, array[N, float]]
Vector[N: static Positive] = array[N, float]
####################################################################################################
# Templates.
template `[]`(m: SquareMatrix; i, j: Natural): float =
## Allow to get value of an element using m[i, j] syntax.
m[i][j]
template `[]=`(m: var SquareMatrix; i, j: Natural; val: float) =
## Allow to set value of an element using m[i, j] syntax.
m[i][j] = val
#---------------------------------------------------------------------------------------------------
func det(m: SquareMatrix): float =
## Return the determinant of matrix "m".
var m = m
result = 1
for j in 0..m.high:
var imax = j
for i in (j + 1)..m.high:
if m[i, j] > m[imax, j]:
imax = i
if imax != j:
swap m[iMax], m[j]
result = -result
if abs(m[j, j]) < 1e-12:
return NaN
for i in (j + 1)..m.high:
let mult = -m[i, j] / m[j, j]
for k in 0..m.high:
m[i, k] += mult * m[j, k]
for i in 0..m.high:
result *= m[i, i]
#---------------------------------------------------------------------------------------------------
func cramerSolve(a: SquareMatrix; detA: float; b: Vector; col: Natural): float =
## Apply Cramer rule on matrix "a", using vector "b" to replace column "col".
when a.N != b.N:
{.error: "incompatible matrix and vector sizes".}
else:
var a = a
for i in 0..a.high:
a[i, col] = b[i]
result = det(a) / detA
#———————————————————————————————————————————————————————————————————————————————————————————————————
import strformat
const
A: SquareMatrix[4] = [[2.0, -1.0, 5.0, 1.0],
[3.0, 2.0, 2.0, -6.0],
[1.0, 3.0, 3.0, -1.0],
[5.0, -2.0, -3.0, 3.0]]
B: Vector[4] = [-3.0, -32.0, -47.0, 49.0]
let detA = det(A)
if detA == NaN:
echo "Singular matrix!"
quit(QuitFailure)
for i in 0..A.high:
echo &"{cramerSolve(A, detA, B, i):7.3f}"</lang>
{{out}}
<pre> 2.000
-12.000
-4.000
1.000</pre>
=={{header|PARI/GP}}==
| |||